Master-equation approach to deterministic chaos
- 1 July 1988
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 38 (1), 427-433
- https://doi.org/10.1103/physreva.38.427
Abstract
A class of exact master equations descriptive of a Markovian process is obtained, starting from the Perron-Frobenius equation for a chaotic dynamical system. The conditions that must be satisfied by the initial probability density for the validity of the master equation are derived. The approach employs projection operator techniques and provides one with a dynamical prescription for carrying out coarse-graining in a systematic manner.Keywords
This publication has 16 references indexed in Scilit:
- Chaotic dynamics applied to information processingReports on Progress in Physics, 1986
- Ergodic theory of chaos and strange attractorsReviews of Modern Physics, 1985
- Symbolic Dynamics Approach to Intermittent ChaosProgress of Theoretical Physics, 1983
- Onset of Diffusion and Universal Scaling in Chaotic SystemsPhysical Review Letters, 1982
- On the Foundations of Kinetic TheoryProgress of Theoretical Physics Supplement, 1980
- Invariant measures for Markov maps of the intervalCommunications in Mathematical Physics, 1979
- Bernoulli maps of the intervalIsrael Journal of Mathematics, 1977
- Denumerable Markov ChainsPublished by Springer Nature ,1976
- The ergodic theory of AxiomA flowsInventiones Mathematicae, 1975
- Markov Partitions for Axiom A DiffeomorphismsAmerican Journal of Mathematics, 1970